Hybrid Solvation Models

This hybrid solvation model surrounds the solute with a small number of explicit solvent molecules, and then embeds this cluster into the implicit dielectric field. Local effects are addressed by the full quantum mechanical treatment of the interaction between the solute and the few explicit solvent molecules. Long-range effects are included through the interaction of the cluster with the dielectric field. A decision is still needed as to how many explicit solvent molecules should be included within the cluster, recognizing that each additional solvent molecule increases the size of the calculation and expands the configurational space that must be explored. 

While computers continue to become ever faster and quantum mechanical algorithms become ever more efficient, the bottom line remains that many chemically 

TABLE 13 Calculated (SM6) Dissociation Free Energies (kcal mol ) and Experimental 

Compound AG hnpUcit Solvent AG hnpUcit Solvent -1- One Explicit Water P a Experimental 

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I. A. Topol, G. J. Tawa, S. K. Burt and A. A. Rashin, On the structure and thermodynamics of solvated monoatomic ions using a hybrid solvation model, J. Chem. Phys. Ill (1999) 10998-11014. 

Abstract A comparative description of two different hybrid solvation models is presented, both of... 

Smooth COSMO solvation model. We have recently extended our smooth COSMO solvation model with analytical gradients [71] to work with semiempirical QM and QM/MM methods within the CHARMM and MNDO programs [72, 73], The method is a considerably more stable implementation of the conventional COSMO method for geometry optimizations, transition state searches and potential energy surfaces [72], The method was applied to study dissociative phosphoryl transfer reactions [40], and native and thio-substituted transphosphorylation reactions [73] and compared with density-functional and hybrid QM/MM calculation results. The smooth COSMO method can be formulated as a linear-scaling Green s function approach [72] and was applied to ascertain the contribution of phosphate-phosphate repulsions in linear and bent-form DNA models based on the crystallographic structure of a full turn of DNA in a nucleosome core particle [74],... 

The solvation models are used to predict the properties of small molecules and large biomolecules employing different levels of theory. In the prediction of solvent effect using electronic structure calculation, semiempirical, HF, post-HF, and DFT-based hybrid methods have been widely used [2-11], Since a wealth of literature is... 

Nucleophilic addition of phenolic nucleophiles to l,l-dicyano-2-arylethenes in the gas phase and in water has been studied theoretically" using the semiempirical AMI method and the Cramer-Truhlar solvation model SM2.1. The difference between the Brpnsted coefficients (a" = 0.81 and P" =0.65) determined for the gas-phase reaction is indicative of a small positive transition state imbalance of / = 0.16. For reaction in water the estimates (a" = 0.61 and P" = 0.36, giving I = 0.25) are close to the experimental values (a" = 0.55 and P" = 0.35) obtained with amine bases, and the small imbalance is as expected for a reaction involving no hybridization change at the incipient carbanion site. 

Sato presents an alternative method to both continuum solvation models and hybrid QM/MM or ONIOM approaches. This is represented by the reference interaction site model (RISM) formalism when combined to a QM description of the solute to give the RISM-SCF theory. 

No systematic study of the effect of different solvation models has been performed. A few reports have compared specific cases such as the study of cationic and anionic alanines, which shows a significant improvement in the chemical shift prediction using polarized continuum method (PCM) or better stiU a hybrid solvation approach (Section 1.4.3). However, the linear scaling correction discussed below can often account for the systematic solvent effect and so sometimes one can get away without any solvent computation at all. 

R.A. Bryce, R. Buesnel, I.H. Hillier, and N.A. Burton, A solvation model using a hybrid quantum mechanical/molecular mechanical potential with flucmating solvent charges, Chem. Phys. Lett., 279 (1997), 367-371. 

A comprehensive discussion of hybrid methods and their application is beyond the scope of this article, and we refer the reader to recent reviews in this field [186, 222-224] and to other methodological papers [225-228] for more detailed information. In the following we focus on the use of semiempirical methods in QM/MM approaches and on some conceptual issues. One typical example for the use of hybrid methods is the study of solvent effects through explicit solvation models (see Section III.C). In this case there is an obvious partitioning between the QM part (solute) and the MM part (solvent) of the system, with well-known QM/MM interactions. The effective Hamiltonian is written as the sum of three terms [186,227] ... 

Going beyond the mean-field level, several "hybrid" approaches are now being explored in MD simulations. Examples include a recent model [70] in which the immediate hydration of the solute is modeled explicitly by a layer of water molecules, and the GB model is used to treat the bulk continuum solvent outside the explicit simulation volume. A similar idea was recently found very effective in the context of replica-exchange simulations [71]. An explicit ion/implicit water (PB) solvation model for molecular dynamics of nucleic acids has recently been tested [72]. 

Okur, A., Wickstrom, L., Layten, M., Geney, R., Song, K., Hornak, V., Simmerling, C. Improved efficiency of replica exchange simulations through use of a hybrid explicit /implicit solvation model. 

From the several continuum solvation methods available in the literature, the PCM model and its derivatives seem to be most used for pK calculations. In fact, the best pK results reported so far have been obtained with one of the PCM-based methods. Nevertheless, the fact that these calculations differ in many respects precludes any comparative evaluation of the different solvation models employed. More systematic studies are needed, taking into consideration the level of theory (method and basis sets) employed, the various continuum solvation models, and different classes of compounds. The introduction of solvent molecules into the solute cavity, in order to better represent the short-range solute-solvent interactions, must also be carefully examined. There is no apparent relationship between the structure of the solute and the number of intracavity solvent molecules that best reproduces the solvation energy. Hence, this best number is generally established on a trial-and-error basis. Also, the use of a such hybrid (discrete -I- continuum) description of the solvent molecules seems to be inconsistent with the fact that for some of the solvation models employed, the effects of the first solvation shell have been already incorporated when parameterizing the cavity. 

Having described a hybrid approach that integrates a first-level QM-DFT approximation with a continuum-level implicit APBS solvation model, as a multiparadigm stratagem to study the effects of solvation on reactivity, we now return to describing fiuther approximations to (1). 

In this framework, a generalization of a hybrid explicit/implicit solvation model for the treatment of polarizable molecular systems at different levels of theory has been recently proposed by our group, the so-called GLOB model [33, 34]. Such a... 

Combined Quantum Mechanical and Molecular Mechanical Potentials Combined Quantum Mechanics and Molecular Mechanics Approaches to Chemical and Biochemical Reactivity Diradicals Hybrid Methods Hybrid Quantum Mechanical/Molecular Mechanical (QM/MM) Methods Quantum Mechanical/Molecular Mechanical (QM/MM) Coupled Potentials Quantum Mechanics/Molecular Mechanics (QM/MM) Self-consistent Reaction Field Methods Self-consistent Reaction Field Methods Cavities Solvation Modeling Transition States in Organic Chemistry Ab Initio Transition Structure Optimization Techniques. 

The drive toward reliable quantum mechanical predictions for large molecular systems is well represented in ECC articles by George Bacskay Solvation Modeling), Krishnan Balasub-ramanian Relativistic Effective Core Potential Techniques for Molecules Containing Very Heavy Atoms), Margareta Blomberg Configuration Interaction PCI-X and Applications), and Keiji Morokuma Hybrid Methods). 

The fully solvated model cannot easily be used with the dipole-correction or applied field methods discussed above. The absence of a vacuum layer in the fully solvated model makes dipole moment evaluation and field application impossible within the periodic model. Hybrid approaches, in which the dipole is measured in an unsolvated model and solvation approximated in the fully solvated model, might be considered. However, the advantage of the fully solvated model is its integration within the direct charging of the electrochemical interface. 

The SM1-SM3 methods model solvation in water with various degrees of sophistication. The SM4 method models solvation in alkane solvents. The SM5 method is generalized to model any solvent. The SM5.42R method is designed to work with HF, DFT or hybrid HF/DFT calculations, as well as with AMI or PM3. SM5.42R is implemented using a SCRF algorithm as described below. A description of the differences between these methods can be found in the manual accompanying the AMSOL program and in the reviews listed at the end of this chapter. Available Hamiltonians and solvents are summarized in Table 24.1. 

The incorporation of the generalized Bom model into free energy calculation methods using FEP/TI and A-dynamics was carried out by Banba and Brooks.81 They define the electrostatic solvation energy for the hybrid system as follows... 

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